A company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Due to many causes - vibration, temperature, wear and tear, and the like - the lengths of the pins made by the machine are normally distributed with a mean of 1.012 inches and a standard deviation of 0.018 inch. The customer will buy only those pins with lengths in the interval 1.00 ± 0.02 inch. In other words, the customer wants the length to be 1.00 inch but will accept up to 0.02 inch deviation on either side. This 0.02 inch is known as the tolerance.

1. What percentage of the pins will be acceptable to the customer?

In order to improve percentage accepted, the production manager and the engineers discuss adjusting the population mean and standard deviation of the length of the pins.

2. If the lathe can be adjusted to have the mean of the lengths to any desired value, what should it be adjusted to? Why?

3. Suppose the mean cannot be adjusted, but the standard deviation can be reduced. What maximum value of the standard deviation would make 90% of the parts acceptable to the consumer (Assume the mean to be 1.012)

4. Repeat question 3, with 95% and 99% of the pins acceptable.

5. In practice, which one do you think is easier to adjust, the mean of the standard deviation? Why?

The production manager then considers the costs involved. The cost of resetting the machine to adjust the population mean involves the engineers' time and the cost of productin time lsot. The cost of reducing the population standard deviation involves, in addition to these costs. The cost of overhauling the machine and reengineering the process.

6. Assume it cost $150x2 to decrease the standard deviation by (x/1000) inch. Find the cost of reducing the standard deviation to the values found in questions 3 and 4.

7. Now assume that the mean has been adjusted to the best value found in question 2 at a cost of $80. Calculate the reduction in standard deviation necessary to have 90%, 95%, and 9(% of the parts acceptable. Calculate the respective coasts, as in question 6.

8. Based on your answers to questions 6 and 7, what are your recommended mean and standard deviations?

The Cinergy Corporation sold 35615 million cubic feet of gas to residential customers, an increase of 1.1% over the previous year. Does this information represent descriptive statistics or inferential statistics? Why?

1)If you have a population that has a small sample, but does not meet all of the criteria for the nonparametric test how can you tell what test to use?
2)How might one know if a samples follow a normal distribution?
Please explain each in roughly 100 words please

If one study claimed 7 out of 8 people (88%) surveyed stated they were against gun control and another study claimed 800 out of 1600 people (50%) were against gun control, which result would you feel is more accurate in the sense of describing the attitudes of the general population? Explain.

A regression equation was estimated for result X=20 to 50 and Y= 200 to 500. Using the regression result
Y=4X+150
a. predict Y if X is 51
b. predict Y if X is 80
c. Which of the above results might be suspect, and why?

1. Suppose we collected data from each person in the class on the number of years since their last math class and their anticipated grade for this statistics class. Determine whether descriptive or inferential statistics would be used to answer each of these research questions:
a. What is the average number of years since th

The general form of a regression equation with a single independent variable is.....
Given a one sample z test, if the critical value of z is 2.58 and the computed value is 2.48, it indicates that hte difference between the sample and population values are.....